GaloisGroupUtilities(R)

galfact.spad line 1 [edit on github]

• R : Ring

GaloisGroupUtilities provides several useful functions.

fillPascalTriangle : () -> Void

fillPascalTriangle() fills the stored table.

pascalTriangle : (NonNegativeInteger, Integer) -> R

pascalTriangle(n, r) returns the binomial coefficient C(n, r)=n!/(r! (n-r)!) and stores it in a table to prevent recomputation.

rangePascalTriangle : () -> NonNegativeInteger

rangePascalTriangle() returns the maximal number of lines stored.

rangePascalTriangle : NonNegativeInteger -> NonNegativeInteger

rangePascalTriangle(n) sets the maximal number of lines which are stored and returns the previous value.

safeCeiling : R -> Integer if R has FloatingPointSystem

safeCeiling(x) returns the integer which is greater than any integer with the same floating point number representation.

safeFloor : R -> Integer if R has FloatingPointSystem

safeFloor(x) returns the integer which is lower or equal to the largest integer which has the same floating point number representation.

safetyMargin : () -> NonNegativeInteger if R has FloatingPointSystem

safetyMargin() returns the number of low weight digits we do not trust in the floating point representation (used by safeCeiling).

safetyMargin : NonNegativeInteger -> NonNegativeInteger if R has FloatingPointSystem

safetyMargin(n) sets to n the number of low weight digits we do not trust in the floating point representation and returns the previous value (for use by safeCeiling).

sizePascalTriangle : () -> NonNegativeInteger

sizePascalTriangle() returns the number of entries currently stored in the table.